When you specify saturation output limits and the controller calculation exceeds the specified output limits, the PID controller block will hold the output at the specified limit. However, the integrator output can continue to grow (integrator windup), increasing the difference between the block output and the sum of the block components. Even though the PID controller block's output is bounded, the integral output remains unbounded.
If the sign of the input signal never changes, the integrator continues to integrate until it overflows. The overflow value is the maximum or minimum value for the data type of the integrator output.
To combat these effects an anti-windup method should be used. The PID controller block offers two methods, back calculation, and clamping. Documentation on these two methods can be found below:
An example of when to implement an anti-windup method is provided below:
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